For attachment "Linear 1," I've proven that it is indeed a linear transformation. My question is what does it mean when it says to show T^2=T? What exactly is the T that I am multiplying by itself?

Attachment "Linear 2," I have found A to be [1 2|
|2 5]
How am I supposed to find the fA^-1 it asks for? Do I just take the inverse of the A I found?

3. The attempt at a solution

Show if you apply T twice to a vector then you get the same result as applying it once. That's what T^2 means here. And sure, find the inverse of the matrix A and write out its action on a vector like they did with ##f_A##.